# Maximum normal stress and shear stress

• Engineering
• Moara

#### Moara

Homework Statement
A cantilever with elasticy modulus (##E = 13 \ GPa##) is subjected to the distribution of forces as in figure. The cross section T shaped is indicated in the figure. The moment of inertia with respect to the centroidal axis ##z## is ##1496.45 \cdot 10^6 \cdot mm^4##. In the absence of the distribution of forces, there is a lack of ##0.5 mm## between the bean and the mobile support. Knowing that the bean touches the support with the load distribution, find:
1) The maximum normal stress
2) The value of the maximum shear stress in the body
3) The deflection in the middle of the bean
Relevant Equations
##\sum{F_y} = 0##, ##\sum{M} = 0##
First, I am trying to find the external reactions in A and B, but I have only one equation relating ##V_A## and ##V_B##, what other relation could I use ?
Once I find the reactions, I can find the external moment as well. Then, I may draw the diagram of moments in each cross section and then find the maximum Moment. Using that ##\sigma = -My/I## I can find the maximum normal stress.

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Indeed, maybe we can try to find the general formula for the displacement of the beam and then impose that ##v(4) = -0.5 mm##. With that, I think we may find ##V_A, V_B, M_A## and find the diagram of moments, to find its maximum value

What would the end deflection be if B was not there?

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